US5796837A - Apparatus and method for generating a secure substitution-box immune to cryptanalyses - Google Patents

Apparatus and method for generating a secure substitution-box immune to cryptanalyses Download PDF

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US5796837A
US5796837A US08/780,143 US78014396A US5796837A US 5796837 A US5796837 A US 5796837A US 78014396 A US78014396 A US 78014396A US 5796837 A US5796837 A US 5796837A
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Prior art keywords
box
substitution
condition
boxes
satisfied
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Kwang Jo Kim
Sang Jin Lee
Sang Joon Park
Seung Cheol Goh
Dai Ki Lee
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Electronics and Telecommunications Research Institute ETRI
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F15/00—Digital computers in general; Data processing equipment in general
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
    • H04L9/002—Countermeasures against attacks on cryptographic mechanisms
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
    • H04L9/06—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols the encryption apparatus using shift registers or memories for block-wise or stream coding, e.g. DES systems or RC4; Hash functions; Pseudorandom sequence generators
    • H04L9/0618—Block ciphers, i.e. encrypting groups of characters of a plain text message using fixed encryption transformation
    • H04L9/0625—Block ciphers, i.e. encrypting groups of characters of a plain text message using fixed encryption transformation with splitting of the data block into left and right halves, e.g. Feistel based algorithms, DES, FEAL, IDEA or KASUMI
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L2209/00—Additional information or applications relating to cryptographic mechanisms or cryptographic arrangements for secret or secure communication H04L9/00
    • H04L2209/08—Randomization, e.g. dummy operations or using noise

Definitions

  • This invention relates to an apparatus and method for generating a substitution-box which can be used in a DES (Data Encryption Standard), which is well known as a data security standard system all over the world, more particulary to an apparatus and method for generating a secure substitution-box immune to both differential cryptanalysis and linear cryptanalysis.
  • DES Data Encryption Standard
  • an apparatus for generating a secure substitution-box immune to differential and linear crypt analyses comprises a preprocessor for exchanging a location by the unit of bit while passing the input of 64 bits data to be protected; a parity checker for obtaining 56 bits key information by passing the input of the 64 bits key by byte unit; a key expander for repetitive operation for generating 48 bits information upon receiving the key information; a first to sixteenth operating portion for performing the 16 times of operation for one data from the preprocessor while mixing the data with an expanding key information from the key expander; and a postprocessor for generating an output signal of 64 bits data upon receiving an operated result from the first to sixteenth operating portion.
  • a method for generating a secure substitution-box comprises a first step of checking whether the condition that S(x) should not be equal to S(x ⁇ (11 efg0)) with respect to a value of any efg and all of 6 bits input for any substitution-box is satisfied or not; and a second step of, if it is determined that the condition is satisfied at the first step, selecting and outputting the satisfied substitution-box, if it is determinded that the condition is not satisfied at the first step, selecting and outputting the non-satisfied substitution-box.
  • a method for generating a secure substitution-box comprises determining whether the corresponding condition (D1) of the apparatus for generating the secure substitution-box immune to linear cryptanalysis and then outputting a satisfied substitution-box.
  • FIG. 1 is a schematic diagram of a general information security system to which this invention is applicable.
  • FIG. 2 is a schematic diagram of a block encryption system in the form of DES to which this invention is applicable.
  • FIG. 3 is a schematic diagram of a repetition operating portion in DES to which this invention is applicable.
  • FIG. 4 is a schematic diagram of a substitution-box of the repetition operating portion in DES to which this invention is applicable.
  • FIG. 5 is an exemplary view of the substitution-box.
  • FIG. 6 is a flowchart for illustrating a D1 condition check.
  • FIG. 7 is a flowchart for illustrating an L1 condition check.
  • FIG. 8 is a flowchart for illustrating an L2 condition check.
  • FIG. 9 is a flowchart for illustrating an L3 condition check.
  • FIGS. 10A and 10B are flowcharts for illustrating an L4 condition check.
  • FIG. 11 is a flowchart for illustrating an L5 condition check.
  • FIG. 12 is a flowchart for illustrating an L6 condition check.
  • FIGS. 13A and 13B are flowcharts for illustrating the generation of 8 substitution-boxes according to the present invention.
  • FIGS. 14A to 14H are exemplary views of 8 substitution-boxes generated, according to the present invention.
  • FIG. 1 shows a schematic diagram of a general information security system to which the present invention is applicable.
  • the information in the form of plain text 101 stored in the computer is subject to the transformation into encryption 102 for creating an encrypted text by use of a key 103 transmitted in advance over a secure communication path 107 between a transmitter and a receiver and then is transmitted to the other party desired for communication.
  • a third party rather than an authorized transceiver may intercept the encrypted text at his disposal, he can not restore an original information legitimately because he does not know the key information.
  • the receiver who had the key information previously delivered to his own can perform the transformation into decryption 105 as an inverse transformation of the transformation into encryption to obtain a decrypted text identical with the original plain text.
  • FIG. 2 shows the known DES algorithm to which this invention is applicable. A description about the operation of the system is below.
  • An input of DES is a 64 bits data input 201 to be protected and a 64 bits key input information 202 delivered legitimately and an oupput of DES is a transformed encryted text 208.
  • the 64 bits data input 201 is exchanged in the location of the bits by bit unit while passing a preprocessor 203.
  • the 64 bits key input 202 passes by byte unit through a parity checker 209 to obtain a substantial key information with 56 bits and then this obtained information provides 48 bits used every repetition operation via a key expander 210 for repetition operation which generates 48 bits information used in a repetitive operating portion.
  • the data preprocessed above is processed with mixed by being the 48-bit expanded key information 16 times through a first operating portion 204, a second operating portion 205, . . . , to a sixteenth operating portion 206.
  • B2 operating portions divide 64 bits into two 32 bits halves. The 32 bits information in right-side of the two being 32 bits output through the repetition operating portion to be described below, and the 32 bits information in left-side of the two being subject to the operation of the exclusive or sum by bit unit and exchanging the information of 32 bit unit to again be the input of the next repetition operating portion.
  • the transformation into the encryption is essentially equal to the transformation into the decryption but may use an expanded key information in a reverse order.
  • FIG. 3 shows a schematic diagram of the repetition operating portion used in the present invention.
  • the 32 bits input 301 of the repetition operating portion is expanded to 48 bits by a 32 to 48 expander 302.
  • the 32 bits input is a1, a2, . . . , a32
  • these bits become a32 , a1, a2, . . . , a5, a6, a5, a6, a7, . . . , a31, a32 to be 48 bits.
  • the 48 bits information is subject to the operation of the Exclusive OR with the expanded key 304 with 48 bits for the repetition operation by bit unit and then the result is divided into eight by the unit of 6 bits. Thereafter, each 6 bits is inputted to a first substitution-box 305, a second substitution-box 306, . . . , an eighth substitution-box 307, respectively and then outputted as 4 bits unit from the respective substitution-boxes. These eight 4 bits units are combined each other to obtain 32 bits information and then pass through a location exchanger 308 by bit unit to obtain an output 309 of the 32 bits repetition operating portion.
  • FIG. 4 shows a schematic diagram of a substitution-box to which the present invention is applicable.
  • Eight substitution-boxes have identical structure, each being formed of four substitution tables 403 with integer numbers from 0 to 15 as elements.
  • bit b0 and b5 of 6 bits input, b0, b1, . . . , b5 are combined to select an input 401 among four substitution tables 403 and the middle 4 bits, i.e., b1, b2, b3, b4 of 6 bits input designates an address of one substitution table value of four substitution table, thereby outputting a stored value therein.
  • FIG. 5 illustrates one of the existing 8 6 ⁇ 4 substitution-boxes in DES.
  • an input is 100011 in binary number
  • bit b0 and b5 are combined to be 11 in binary number and 3 in decimal number. Accordingly, a third row 501 is selected. Then, because the middle 4 bits 0001 of the input is 1 in decimal number, the first value 502 of the third substitution table is read out to be outputted as 12 in decimal number, i.e., 1100 in binary number.
  • substitution-box is expressed in a mathemical symbol, it is S(x): Z 2 6 A ⁇ Z 2 4 which plays the most inportant role in DES.
  • FIG. 6 shows a flowchart for checking the condition D1 related the differential cryptanalysis.
  • a condition should be given such that the change of the input of all 8 substitution-boxes causes the change of their output.
  • S(x) should be not equal to S(x ⁇ (11 efg 0)) (step 607) and a substitution-box for which this condition is satisfied are chosen (step 614).
  • the first step of the linear cryptanalysis method is to compute a linear distribution table of the substitution-box. If 6 bits input and 4 bits output which are masked are indicated as ⁇ and ⁇ , respectively, a linear distribution table NS( ⁇ , ⁇ ) is defined for any substitution-box S(x) as follows:
  • FIG. 7 shows a flowchart for checking an L1 condition as one of the condition required to generate a secure substitution-box immune to the linear cryptanalysis. More specifically, any random 6 ⁇ 4 substitution-box is read out (step 702) and then its linear distribution table is calculated (step 703). Thereafter, if it is determined that m is less than 16, a 6 ⁇ 4 substitution-box for which L1 condition is satisfied is outputted (step 705), if it is determined that m exceeds the maximum value 16, a substitution-box for which the L1 condition is not satisfied is outputted (step 706).
  • FIG. 8 shows a flowchart for checking an L2 condition as one of the condition required to generate a secure substitution-box immune to the linear cryptanalysis. More specifically, for a and b with the count of 1 less than two on the linear distribution table (step 803) of any substitution-box (step 802), as a condition to minimize a linear repetition characteristics, if it is determined that an absolute value of the linear distribution table,
  • FIG. 9 shows a flowchart for checking an L3 condition as one of the conditions required to generate a secure substitution-box immune to the linear cryptanalysis.
  • FIGS. 10A and 10B show flowcharts for checking an L4 condition as one of the conditions required to generate a secure substitution-box immune to the linear cryptanalysis.
  • NS1(a, b) for any substitution box is calculated (step 1007), and if it is determined that values of NS1 (4, 4) and NS1 (2, 2) of the 8 substitution-boxes are 0(step 1011), a first substitution-box for which the L4 condition is satisfied is outputted (step 1015).
  • NS2(a, b) for any substitution box is calculated (step 1008), and if it is determined that values of NS2(4, 4) and NS2(2, 1) of the 8 substitution-boxes are 0(step 1012), a second substitution-box for which the L4 condition is satisfied is outputted (step 1016).
  • NS3(a, b) for any substitution box is calculated (step 1009), and if it is determined that values of NS 3 (8, 4) and NS3 (4, 8) of the 8 substitution-boxes are 0(step 1013), a third substitution-box for which the L4 condition is satisfied is outputted (step 1017).
  • NS4(a, b) for any substitution box is calculated (step 1010), and if it is determined that values of NS4(8, 4) and NS4(2, 2) of the 8 substitution-boxes are 0(step 1014), a fourth substitution-box for which the L4 condition is satisfied is outputted (step 1018).
  • NS5(a, b) for any substitution box is calculated (step 1023), and if it is determined that values of NS5 (16, 1) and NS5 (8, 8) of the 8 substitution-boxes are 0(step 1027), a fifth substitution-box for which the L4 condition is satisfied is outputted (step 1031).
  • NS6(a, b) for any substitution box is calculated (step 1024), and if it is determined that values of NS6(16, 4) and NS6(4, 8) of the 8 substitution-boxes are 0(step 1028), a sixth substitution-box for which the L4 condition is satisfied is outputted (step 1032).
  • NS7(a, b) for any substitution box is calculated (step 1035), and if it is determined that values of NS7 (4, 8) and NS7 (2, 1) of the 8 substitution-boxes are 0(step 1029), a seventh substitution-box for which the L4 condition is satisfied is outputted (step 1033).
  • NS8(a, b) for any substitution box is calculated (step 1026), and if it is determined that values of NS8(16, 1) and NS8(2, 4) of the 8 substitution-boxes are 0(step 1030), an eighth substitution-box for which the L4 condition is satisfied is outputted (step 1034).
  • FIG. 11 shows a flowchart for checking a special condition (L5) for generating the fifth substitution-box and the eighth substitution-box to minimize the linear repetition characteristics.
  • L5 special condition
  • the linear distribution tables NSj (a, b) of the fifth and eighth substitution-boxes are calculated (step 1103) and a value of exclusive OR of a with an input mask value of 16 (step 1104) and two output mask values b1 and b2 is 1, if it is determined that an absolute value of the multiplication of NSj (a, b1) and NSj(a, b2) is less than 48 (step 1105), the fifth and eighth substitution-boxes for which the L5 condition is satisfied is outputted (step 1106).
  • FIG. 12 shows a flowchart for checking a special condition (L6) for generating the sixth substitution-box to minimize the linear repetition characteristics.
  • L6 special condition
  • FIGS. 13A and 13B show flowcharts for illustrating the generation of 8 substitution-boxes according to the present invention.
  • random substitution is produced (step 1303) and then four substitutions are selected so that a sufficient number of a candidate substitution box is generated (step 1304).
  • substitution-boxes For each of substitution-box, individual substitution-boxes for which the D1 condition (step 1305), the L1 condition (step 1306), the L2 condition (step 1307), and the L3 condition (step 1308) are satisfied are generated. Then, substitution-boxes for which the L5 condition (step 1309) and the L6 condition (step 1310) are satisfied is generated as candidates of the fifth, sixth, and eighth substitution-boxes. Finally, by checking the L4 condition (step 1311), each of 8 substitution-boxes is generated (step 1312).
  • FIGS. 14A to 14H show exemplary views of 8 substitution-boxes generated, according to the present invention.
  • the differential cryptanalysis and the linear cryptanalysis are not applicable to DES.
  • substitution-boxes to be inserted are used in individualization, an individual security system is constructed so that a variety of the system is realized.

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Cited By (17)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US6031911A (en) * 1996-07-18 2000-02-29 Entrust Technologies, Ltd. Practical S box design
DE19845073A1 (de) * 1998-09-30 2000-04-06 Siemens Ag Verfahren zur Absicherung der DES-Verschlüsselung gegen Ausspähung der Schlüssel durch Analyse der Stromaufnahme des Prozessors
WO2001008012A1 (en) * 1999-07-26 2001-02-01 Motorola Inc. Method and apparatus for preventing information leakage attacks on a microelectronic assembly
US20010019610A1 (en) * 2000-01-26 2001-09-06 Takeshi Shimoyama Method and apparatus for designing cipher logic, and a computer product
US20020021802A1 (en) * 2000-07-12 2002-02-21 Hirofumi Muratani Encryption apparatus, decryption appatatus, expanded key generating apparatus and method therefor, and recording medium
US20020027987A1 (en) * 2000-07-04 2002-03-07 Roelse Petrus Lambertus Adriaanus Substitution-box for symmetric-key ciphers
US20020061107A1 (en) * 2000-09-25 2002-05-23 Tham Terry K. Methods and apparatus for implementing a cryptography engine
US20020078342A1 (en) * 2000-09-25 2002-06-20 Broadcom Corporation E-commerce security processor alignment logic
US20030068038A1 (en) * 2001-09-28 2003-04-10 Bedros Hanounik Method and apparatus for encrypting data
US20030118190A1 (en) * 1998-05-29 2003-06-26 Siemens Aktiengesellschaft Method and apparatus for processing data where a part of the current supplied is supplied to an auxiliary circuit
US7076059B1 (en) * 2002-01-17 2006-07-11 Cavium Networks Method and apparatus to implement the data encryption standard algorithm
US7103180B1 (en) * 2001-10-25 2006-09-05 Hewlett-Packard Development Company, L.P. Method of implementing the data encryption standard with reduced computation
US7187769B1 (en) * 1998-06-02 2007-03-06 Nippon Telegraph And Telephone Public Corporation Method and apparatus for evaluating the strength of an encryption
US7292693B1 (en) * 1998-08-13 2007-11-06 Teledyne Technologies Incorporated Deterministically generating block substitution tables which meet a given standard of nonlinearity
US7477741B1 (en) 2004-10-01 2009-01-13 The United States Of America As Represented By The Administrator Of The National Aeronautics And Space Administration Analysis resistant cipher method and apparatus
US20110129085A1 (en) * 2009-12-01 2011-06-02 Samsung Electronics Co., Ltd. Cryptographic device for implementing s-box
US20160065361A1 (en) * 2014-08-28 2016-03-03 Samsung Electronics Co., Ltd. Endecryptor preventing side channel attack, driving method thereof and control device having the same

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US4275265A (en) * 1978-10-02 1981-06-23 Wisconsin Alumni Research Foundation Complete substitution permutation enciphering and deciphering circuit
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Cited By (26)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US6031911A (en) * 1996-07-18 2000-02-29 Entrust Technologies, Ltd. Practical S box design
US20030118190A1 (en) * 1998-05-29 2003-06-26 Siemens Aktiengesellschaft Method and apparatus for processing data where a part of the current supplied is supplied to an auxiliary circuit
US7187769B1 (en) * 1998-06-02 2007-03-06 Nippon Telegraph And Telephone Public Corporation Method and apparatus for evaluating the strength of an encryption
US7292693B1 (en) * 1998-08-13 2007-11-06 Teledyne Technologies Incorporated Deterministically generating block substitution tables which meet a given standard of nonlinearity
DE19845073A1 (de) * 1998-09-30 2000-04-06 Siemens Ag Verfahren zur Absicherung der DES-Verschlüsselung gegen Ausspähung der Schlüssel durch Analyse der Stromaufnahme des Prozessors
DE19845073C2 (de) * 1998-09-30 2001-08-30 Infineon Technologies Ag Verfahren zur Absicherung der DES-Verschlüsselung gegen Ausspähung der Schlüssel durch Analyse der Stromaufnahme des Prozessors
WO2001008012A1 (en) * 1999-07-26 2001-02-01 Motorola Inc. Method and apparatus for preventing information leakage attacks on a microelectronic assembly
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US20010019610A1 (en) * 2000-01-26 2001-09-06 Takeshi Shimoyama Method and apparatus for designing cipher logic, and a computer product
US7346161B2 (en) * 2000-01-26 2008-03-18 Fujitsu Limited Method and apparatus for designing cipher logic, and a computer product
US7043016B2 (en) * 2000-07-04 2006-05-09 Koninklijke Philips Electronics N.V. Substitution-box for symmetric-key ciphers
US20020027987A1 (en) * 2000-07-04 2002-03-07 Roelse Petrus Lambertus Adriaanus Substitution-box for symmetric-key ciphers
US7194090B2 (en) * 2000-07-12 2007-03-20 Kabushiki Kaisha Toshiba Encryption apparatus, decryption apparatus, expanded key generating apparatus and method therefor, and recording medium
US20020021802A1 (en) * 2000-07-12 2002-02-21 Hirofumi Muratani Encryption apparatus, decryption appatatus, expanded key generating apparatus and method therefor, and recording medium
US7555121B2 (en) 2000-09-25 2009-06-30 Broadcom Corporation Methods and apparatus for implementing a cryptography engine
US20020061107A1 (en) * 2000-09-25 2002-05-23 Tham Terry K. Methods and apparatus for implementing a cryptography engine
US20020078342A1 (en) * 2000-09-25 2002-06-20 Broadcom Corporation E-commerce security processor alignment logic
US20030068038A1 (en) * 2001-09-28 2003-04-10 Bedros Hanounik Method and apparatus for encrypting data
US7103180B1 (en) * 2001-10-25 2006-09-05 Hewlett-Packard Development Company, L.P. Method of implementing the data encryption standard with reduced computation
US7076059B1 (en) * 2002-01-17 2006-07-11 Cavium Networks Method and apparatus to implement the data encryption standard algorithm
US7477741B1 (en) 2004-10-01 2009-01-13 The United States Of America As Represented By The Administrator Of The National Aeronautics And Space Administration Analysis resistant cipher method and apparatus
US20110129085A1 (en) * 2009-12-01 2011-06-02 Samsung Electronics Co., Ltd. Cryptographic device for implementing s-box
US8750497B2 (en) * 2009-12-01 2014-06-10 Samsung Electronics Co., Ltd. Cryptographic device for implementing S-box
US9344273B2 (en) 2009-12-01 2016-05-17 Samsung Electronics Co., Ltd. Cryptographic device for implementing S-box
US20160065361A1 (en) * 2014-08-28 2016-03-03 Samsung Electronics Co., Ltd. Endecryptor preventing side channel attack, driving method thereof and control device having the same
US10291390B2 (en) 2014-08-28 2019-05-14 Samsung Electronics Co., Ltd. Endecryptor preventing side channel attack, driving method thereof and control device having the same

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